Particle projection

Pulpstones. Improvements have been made in the composition and speed of the grinding wheel, in methods of feeding the wood and pressing it against the stone, in control of power to the stones, and in the size and capacity of the units. The first pulpstones were manufactured from quarried sandstone, but have been replaced by carbide and alumina embedded in a softer ceramic matrix, in which the harder grit particles project from the surface of the wheel (see Abrasives). The abrasive segments ate made up of three basic manufactured abrasive siUcon carbide, aluminum oxide, or a modified aluminum oxide. Synthetic stones have the mechanical strength to operate at peripheral surface speeds of about 1200—1400 m /min (3900 to 4600 ft/min) under conditions that consume 0.37—3.7 MJ/s (500—5000 hp) pet stone. 

A area of particle projected in direction of motion plan area of settling tank or thickener... 

FIG. 6-57 Drag coefficients for spheres, disks, and cylinders =area of particle projected on a plane normal to direction of motion C = over-... 

Cross-sectional aiea allocated to light phase, sq ft Area of particle projected on plane normal to direction of flow or motion, sq ft Cross-sectional area at top of V essel occupied by continuous hydrocarbon phase, sq ft Actual flow at conditions, cu ft/sec Constant given in table Volume fiaction solids Overall drag coefficient, dimensionless Diameter of vessel, ft See Dp, min Cyclone diameter, ft Cyclone gas exit duct diameter, ft Hy draulic diameter, ft = 4 (flow area for phase in qiiestion/wetted perimeter) also, D in decanter design represents diameter for heavy phase, ft... 

Ap-Area of Particle Projected on Plane Normal to Direction of Flow or Motion, sq. ft. 

With roi the particle s center of gravity, this equation defines R2gi by the second central moment of the density distribution of the particle projected on a line extending in r direction. The equation is simplified (ro = 0) if the origin of the coordinate system is chosen to rest in the center of gravity. 

Efficiencies or efficiency factors Q are defined by dividing the cross-section by the cross-sectional area of the particle projected onto the plane perpendicular to the incident beam. For a spherical particle of radius a one writes... 

Unlike the sphericity, can be determined from microscopic or photographic observation. Use of is only justified on empirical grounds, but it has the potential advantage of allowing correlation of the dependence of flow behavior on particle orientation. For an axisymmetric particle projected parallel to its axis, is unity. 

The additional complexity is not limited to introduction of two new groups. For example, Eq. (11-3) takes different forms for a particle accelerating from rest and a particle projected in a stagnant fluid. In principle, all time derivatives... 

With these simplifications, W and X can be generated as functions of T, with the particle characterized by a single dimensionless parameter, either Rejs, A d or Rqj. Figure 11.13 shows predictions for a particle released from rest W = X = 0 at T = 0), while Fig. 11.14 gives trajectories for particles projected vertically upwards such that the particle comes to rest at T = 0. Figures 11.13 and 11.14 enable rapid estimations for many problems involving unsteady motion of particles in gases. 

Much has been written on the solution of Eqs. (11-74) and (11-75) [see, e.g., (H8, K4, Ml3)], frequently without serious consideration of the validity of Type 2 simplifications. Approximate methods, avoiding numerical integration, are also available for specific types of motion, such as a particle projected with arbitrary velocity in a gravitational field (H8, K4). 

Apr = the area of the particle projected on a plane normal to the direction of flow (projected area perpendicular to flow) ula. = the terminal velocity CD = an empirical drag coefficient. 

FIG. 6-57 Drag coefficients for spheres, disks, and cylinders A = area of particle projected on a plane normal to direction of motion C = overall drag coefficient, dimensionless Dp - diameter of particle Fd = drag or resistance to motion of body in fluid Re = Reynolds number, dimensionless u = relative velocity between particle and main body of fluid (I = fluid viscosity and p = fluid density. (From Lapple and Shepherd, Ind. Eng. Chem., 32, 60S [1940].)... 

Experimental data were embodied in tables presenting C Re in terms of Re/Cf) and vice versa. Since the former expression is independent of velocity and the latter is independent of particle diameter, the velocity may be determined for a particle of known diameter and the diameter determined for a known settling velocity. Heywood also presented data for non-spherical particles in the form of correction tables for four values of volume-shape coefficient from microscopic measurement of particle-projected areas. 

In addition, initial 3D maps of yet uncharacterized, but reproducibly observed complexes can be obtained from projections of negatively stained samples. Ultimately, the visual proteomics chain will be completed by the inspection of vitrified cell fractions, using cryo-electron microscopy. By sorting out particle projections based on all information established with mass-mapping and 3D reconstruction of negatively stained complexes, high-resolution 3D maps will be obtained. Combined with mass spectrometry data from the respective fractions, these 3D maps will provide a solid foundation for creating atomic scale models of all complexes identified. 

For example, particles can be photographed and the area of the particle projection can be measured. The equivalent diameter of a hypothetical sphere with the same projection area can then be calculated (Figure 21). In similar ways, other equivalent diameters can be determined such as diameters equivalent to spheres with the same volume, mass, specific surface area, sedimentation velocity in gases or liquids, etc. Sometimes, equivalent diameters are not unequivocal and may be limited in validity by the assumptions on which the physical models are based. 

Evidence tor both mechanisms based on numerical computations has been reponed by Chen and McLaughlin (1995). They found a bimodal distribution in Ihe impact velocities of pitrticles striking the wall for r+ = 10. They associated the peak velocities of 0.3 , and with particles projected from the core and particles transported by eddy diffusion, respectively. Chen and McLaughlin (1995) and other investigators also report that numerical simulations indicate that panicle concentrations near the wall are higher than oineeniraiions in the turbulent core. 

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